$\dfrac{ i + 10j }{ -5 } = \dfrac{ 9i + 2k }{ -6 }$ Solve for $i$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ i + 10j }{ -{5} } = \dfrac{ 9i + 2k }{ -6 }$ $-{5} \cdot \dfrac{ i + 10j }{ -{5} } = -{5} \cdot \dfrac{ 9i + 2k }{ -6 }$ $i + 10j = -{5} \cdot \dfrac { 9i + 2k }{ -6 }$ Multiply both sides by the right denominator. $i + 10j = -5 \cdot \dfrac{ 9i + 2k }{ -{6} }$ $-{6} \cdot \left( i + 10j \right) = -{6} \cdot -5 \cdot \dfrac{ 9i + 2k }{ -{6} }$ $-{6} \cdot \left( i + 10j \right) = -5 \cdot \left( 9i + 2k \right)$ Distribute both sides $-{6} \cdot \left( i + 10j \right) = -{5} \cdot \left( 9i + 2k \right)$ $-{6}i - {60}j = -{45}i - {10}k$ Combine $i$ terms on the left. $-{6i} - 60j = -{45i} - 10k$ ${39i} - 60j = -10k$ Move the $j$ term to the right. $39i - {60j} = -10k$ $39i = -10k + {60j}$ Isolate $i$ by dividing both sides by its coefficient. ${39}i = -10k + 60j$ $i = \dfrac{ -10k + 60j }{ {39} }$